Bell’s theorem without inequalities

Greenberger, Daniel M.; Horne, Maria; Shimony, Abner; Zeilinger, Anton

doi:10.1119/1.16243

Cited by 2,250 publications

(1,767 citation statements)

References 0 publications

Supporting

Mentioning

1,719

Contrasting

Unclassified

Order By: Relevance

“…When three particles are prepared in the quantum state known as the GHZ state, there are three observables X 1 , X 2 and X 3 , each corresponding to one particle, and taking one of two possible values +1 or −1, such that the product of the revealed outcomes must equal −1 (for details see Greenberger et al 1990;Bigaj 2006, pp. 143-145).…”

Section: Bennett's Fork Theorymentioning

confidence: 99%

How to evaluate counterfactuals in the quantum world

Bigaj

2012

Synthese

View full text Add to dashboard Cite

In the article I discuss possible amendments and corrections to Lewis's semantics for counterfactuals that are necessary in order to account for the indeterministic and non-local character of the quantum world. I argue that Lewis's criteria of similarity between possible worlds produce incorrect valuations for alternate-outcome counterfactuals in the EPR case. Later I discuss an alternative semantics which rejects the notion of miraculous events and relies entirely on the comparison of the agreement with respect to individual facts. However, a controversy exists whether to include future indeterministic events in the criteria of similarity. J. Bennett has suggested that an indeterministic event count toward similarity only if it is a result of the same causal chain as in the actual world. I claim that a much better agreement with the demands of the quantum-mechanical indeterminism can be achieved when we stipulate that possible worlds which differ only with respect to indeterministic facts that take place after the antecedent-event should always be treated as equally similar to the actual world. In the article I analyze and dismiss some common-sense counterexamples to this claim. Finally, I critically evaluate Bennett's proposal regarding the truth-conditions for true-antecedent counterfactuals.

show abstract

Section: Bennett's Fork Theorymentioning

confidence: 99%

How to evaluate counterfactuals in the quantum world

Bigaj

2012

Synthese

View full text Add to dashboard Cite

show abstract

“…As a result, it is the so-called "classical" version of the CHSH inequality-and most if not all of the other guises that Bell's inequalities can take on-that is suspect. (This includes versions that do not directly involve inequalities, such as the GHZ formulation, [26] but which require statistical arguments when experimental justification is sought. This is covered in more detail in a previous paper.…”

Section: E(qs) + E(rs) + E(rt ) − E(qt ) ≤mentioning

confidence: 99%

Nonlinearities in quantum mechanics

McHarris

2005

Braz. J. Phys.

View full text Add to dashboard Cite

Many of the paradoxes encountered in the Copenhagen interpretation of quantum mechanics can be shown to have plausible, more logical parallels in terms of nonlinear dynamics and chaos. These include the statistical exponential decay laws, interpretations of Bell's inequalities, spontaneous symmetry breaking, and perhaps diffractive behavior and even quantization itself. Many of the so-called alternative explanations of quantum mechanics have toyed with ideas that approach chaotic behavior, but as they were formulated before the advent of modern chaos theory, they remained within linear systems or at most nonlinear perturbations to linear systems; however, only strongly nonlinear systems can provide the proper parallels to the Copenhagen paradoxes. Several examples of these will be covered qualitatively. Strongly nonlinear behavior related to quantum mechanics does not involve "hidden variables," but chaos provides a bridge between the statistical behavior of quantum mechanics and deterministic behavior of classical mechanics. Perhaps both Einstein and Bohr were correct in their debates-chaos fundamentally provides the determinism so dear to Einstein, but in practice it must be interpreted statistically in the manner of Bohr.

show abstract

“…It is composed out of two semi-classical, distinct states, each of which a direct product of two coherent states in, in total, four mutually orthogonal modes, i.e., |χ is a "cat state" [109]. It is an entangled coherent state with nonclassical correlations of the GHZ type [57,[117][118][119]. From an experimental point of view, handling |χ may prove difficult: the state will be very sensitive to decoherence, and its creation requires a special, highly nonlinear MZI that, at the time of this writing, is not readily available.…”

Section: The Simultaneously Both Open and Closed Configurationmentioning

confidence: 99%

An Approach To “Quantumness” In Coherent Control

Scholak

Brumer

2017

Advances in Chemical Physics

View full text Add to dashboard Cite

Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc.. Here we introduce and utilize these tools to examine the role of quantum coherence and nonclassical effects in 1 vs. N photon coherent phase control, a paradigm for an all-optical method for manipulating molecular dynamics. In addition, truly quantum control scenarios are introduced and examined. The approach adopted here serves as a template for studies of the role of quantum mechanics in other coherent control and optimal control scenarios.

show abstract

Bell’s theorem without inequalities

Cited by 2,250 publications

References 0 publications

How to evaluate counterfactuals in the quantum world

How to evaluate counterfactuals in the quantum world

Nonlinearities in quantum mechanics

An Approach To “Quantumness” In Coherent Control

Contact Info

Product

Resources

About